Calculate The Original Price: A Math Problem

Hey guys! Let's dive into a classic math problem that often pops up in everyday life: calculating the original price after a percentage increase. This is super useful, whether you're shopping, budgeting, or just trying to understand how prices change. In this article, we'll break down the problem, step by step, so you can easily solve it.

We will be discussing a scenario where a hairdryer has increased in price. We will start with a breakdown of the question, look at the method to solve this, and the steps to solve it. After this, we will dive into more examples to help you solidify your understanding of this topic. I promise, by the end of this, you will be a pro at solving these types of problems. So, buckle up, and let's get started!

Understanding the Problem: The Hairdryer's Price Hike

Alright, let's look at the actual problem. A hairdryer's price went up by 15%, and now it costs 2645 rubles. The question is: What was the original price of the hairdryer before the increase? This type of question is very common, so being able to solve this is very important.

• The Increase: The price rose by 15%. This means the new price is the old price plus 15% of the old price.
• The New Price: The current price is 2645 rubles. This is the price after the increase.
• The Goal: Find the original price before the increase. This is what we need to figure out.

To solve this, we will use a very easy method. First, let's represent the original price with a variable, let's say 'x'. The increase is 15% of 'x', which can be written as 0.15x. The new price is the original price plus the increase, which gives us the equation: x + 0.15x = 2645. Now, to solve this equation, you can see how straightforward it is, but we will go through it to make sure we don't leave any room for doubt.

Now, the equation will be simplified to 1.15x = 2645. Then, to find the value of 'x' (the original price), we divide both sides of the equation by 1.15. This gives us x = 2645 / 1.15. Doing the calculation, we find that x = 2300. Thus, the original price of the hairdryer was 2300 rubles. Now that we have covered the basics, let's go into more detailed information.

The Importance of Percentages in Price Calculations

Understanding percentages is crucial when dealing with price increases and decreases. Percentages are simply a way to express a proportion of a whole. In this case, the price increase is a percentage of the original price. This is why knowing how to work with percentages helps. Let's make sure we have the basics down. To calculate a percentage of a number, you convert the percentage to a decimal (by dividing by 100) and multiply it by the number. For instance, to find 15% of 2000 rubles, you would calculate 0.15 * 2000 = 300 rubles. This is the amount of the increase, not the final price. The final price is the original price plus the increase. Being able to easily calculate percentages is very important for many real-world things.

The Calculation: Breaking Down the Steps

Let's go through the solution in a step-by-step manner. I will break down each step so that you guys can easily follow along and understand what is happening. We already discussed the basic breakdown of the problem, so let's get into it.

Step-by-Step Solution

1. Represent the Original Price: Let 'x' be the original price of the hairdryer. This is the unknown value we are trying to find. We are trying to find the value of x.
2. Calculate the Increase: The price increased by 15%, so the increase is 0.15 * x. This is the amount added to the original price.
3. Set Up the Equation: The new price (2645 rubles) is the original price ('x') plus the increase (0.15x). Thus, the equation is: x + 0.15x = 2645. We are using all the information we have been provided to solve for x.
4. Simplify the Equation: Combine the 'x' terms: 1x + 0.15x = 1.15x. So, the equation becomes: 1.15x = 2645. Make sure you don't make a mistake when simplifying the equation, as this can affect your final answer.
5. Solve for 'x': Divide both sides of the equation by 1.15: x = 2645 / 1.15. The equation is almost done, just a couple more steps.
6. Calculate the Answer: x = 2300. This means the original price of the hairdryer was 2300 rubles. We solved for x, and now we know the answer.

Understanding the Formula

While the step-by-step method is great for understanding, we can also use a formula. If the new price is the original price plus a percentage increase, we can use the formula:

Original Price = New Price / (1 + Percentage Increase as a Decimal).

In our case, the new price is 2645 rubles, and the percentage increase is 15% (or 0.15 as a decimal). Thus, the formula looks like this: Original Price = 2645 / (1 + 0.15). Solving this gives us 2645 / 1.15 = 2300 rubles. There are often multiple ways to solve a math problem, but as long as we understand the steps, we can always solve it.

Practical Examples and Applications

This kind of problem comes up all the time. Let's look at some other examples to get you guys comfortable with solving problems like these.

Example 1: Discounted Items

Suppose a shirt is on sale for 20% off, and the sale price is 800 rubles. What was the original price? In this case, the sale price is 80% of the original price (100% - 20% discount = 80%).

To solve this, we can set up the equation: 0.80x = 800. Divide both sides by 0.80 to find x = 1000. So, the original price of the shirt was 1000 rubles. You can see how easy it is to manipulate the equations to find the answer.

Example 2: Inflation and Price Adjustments

Imagine the price of a certain product increased by 5% due to inflation, and it now costs 1050 rubles. What was the original price before the increase? Here, we know that the new price is 105% of the original price (100% + 5% increase = 105%). The equation will be 1.05x = 1050. Dividing both sides by 1.05, we get x = 1000. Therefore, the original price was 1000 rubles. Inflation can affect how you manage your money, and knowing how to do these equations can help you with this.

Where You'll See This in Real Life

• Shopping: Calculating the original price of items on sale.
• Personal Finance: Budgeting and understanding how prices change over time.
• Investments: Analyzing the return on investments after fees and gains.
• Business: Pricing strategies and understanding profit margins.

These types of calculations are also very common in real life and are very useful. I suggest you guys try these problems and practice to solidify the knowledge. You will find that knowing this is very useful in your daily life.

Tips for Solving Price Increase Problems

Here are some tips to make solving these problems easier:

• Always identify what you know: What is the new price? What is the percentage increase or decrease?
• Convert percentages to decimals: Divide the percentage by 100.
• Set up the equation correctly: Make sure you correctly represent the relationship between the original price, the increase/decrease, and the new price.
• Double-check your work: Make sure your answer makes sense in the context of the problem. A hairdryer cannot be negative, so make sure to check the answer.

By following these steps and practicing, you'll become a pro at solving these problems. Keep in mind that practice is key, and the more problems you solve, the more comfortable you'll become. So, keep at it!

Conclusion: Mastering the Price Increase Calculation

Alright, guys, you've now learned how to calculate the original price after a percentage increase. We've covered the basics, walked through a step-by-step solution, and explored different scenarios. Remember to break down the problem, identify the knowns, and use the appropriate formula. With practice, you'll be able to solve these types of problems with ease.

So go out there, practice, and apply your new skills. You've got this! And remember, if you have any questions or want to try some more examples, feel free to ask. Keep learning, and keep growing! Also, share this with your friends, so they can also benefit from this guide. Thanks for reading, and have a great day!